Transdermal drug delivery systems (TDDS) offer an innovative and non-invasive solution for delivering medications directly through the skin, bypassing systemic side effects and enhancing therapeutic efficacy. This paper presents the design and development of an ultrasound-mediated TDDS, utilizing sonophoresis and cavitation mechanisms to enhance drug permeability. A comprehensive mathematical model based on Fick’s Law, Navier-Stokes equations, acoustic radiation force, ligand-receptor binding dynamics, and temperature dependent effects was developed to simulate drug diffusion and validate hardware design. Simulations reveal significant improvements in drug penetration rates and effective skin permeability, demonstrating the feasibility of the proposed system. Key insights into acoustic, thermal, and biological parameters are provided, paving the way for safer, more efficient drug delivery methods.